16/01/2020

Outline

  • What are our objectives?
  • Why Jamaica Stock Exchange (JSE)
  • Company’s Profile for Portfolio
  • Methodology
  • Analysis
  • Conclusion
  • References

Objective

An investor would like to invest in the JSE, we want to present a model of a diversified portfolio that optimizes returns given the share price movements of the market

Why would an invester want to invest in the JSE?

Motivation for choosing JSE stocks

Best performing stock market in the world for 2015 and again in 2019 by Bloomberg.

Jamaica Stock Exchange (JSE)

Wall street flew the Jamaican flag on Wall street.

Jamaica Stock Exchange (JSE)

Nasdaq to deliver tech to Nasdaq

Scotia Group Jamaica

  • Bank of the Year 2013 and best FX trader in Jamaica
  • Been in Jamaica for over 125 years
  • Banking Services , Insurance, Investments, Mortgage etc.

Caribbean Cement Company

  • Primary cement and gypsum manufacturer & supplier Caribbean
  • 60 year old company
  • Current growth due to boom of the construction industry

Grace Kenedy Group

  • One of the Caribbean’s largest conglomerates
  • Diversified companies in the Caribbean, Europe and North America.

JSE Stocks prices

Scotia Group Jamaica (Jan 2013 - Jan 2020)

JSE Stocks prices

Caribbean Cement Co. (Jan 2013 - Jan 2020)

JSE Stocks prices

Grace Kenedy Group (Jan 2013 - Jan 2020)

Methodology - Definitions

Portfolio Return:

\[R_p = w_1R_1+w_2R_2+...+w_nRn\]

Expected Return:

\[E(R_p) = w_1E(R_1)+w_2E(R_2)+...+w_nE(Rn)\]

Covariance:

\[\sigma^2(R_p)=E[(R_p-E(R_p))^2]\]

Standard Deviation (Risk):

\[\sigma(R_p)=(E[(R_p-E(R_p))^2])^{1/2}\]

Methodology - Markov Chain Model

The sequence of consecutive trials such that:

\[Pr\{X_{n}=j\mid X_{n-1}=i_{n-1}, \dots,X_0=i_o\}\] \[= Pr\{X_{n}=j\mid X_{n-1}=i_{n-1}\}~~~~~~~~\]

Where order of subscripts in \(P_{ij}\) below corresponds to the direction of transition \(i > j\)

\[Pr\{X_{n}=j\mid X_{n-1}=i\}=P_{ij}\]

Analysis - Portfolio specification

ja_folio <- portfolio.spec(assets = colnames(ja_returns))
ja_folio  <- add.constraint(
  portfolio = ja_folio , 
  type = "box", 
  min = 0.05, 
  max = 0.65
)

ja_folio  <- add.constraint(
  portfolio = ja_folio , 
  type = "leverage", # "full_investment"
  min_sum = 0.99,  
  max_sum = 1.01
) 

Analysis - Portfolio specification

Maximize the mean return with ROI

max_return <- add.objective(
  portfolio = ja_folio , 
  type = "return", 
  name = "mean"
) 

Optimize

opt_max_return <- optimize.portfolio(
  R = ja_returns, 
  portfolio = max_return, 
  optimize_method = "ROI",
  trace = TRUE
)

Looking at results

print(opt_max_return$data_summary)
## $first
##              SGJ CCC GK
## 2013-01-02 -0.13   0  0
## 
## $last
##             SGJ  CCC   GK
## 2020-01-13 2.23 1.82 1.02
print(opt_max_return$weights)
##  SGJ  CCC   GK 
## 0.05 0.31 0.65

Plot optimized maximum mean

Minimize variance with Return On Iinvestment (ROI)

min_var <- add.objective(
  portfolio = ja_folio , 
  type = "risk",
  name = "var"
)

Optimize.

Note that although var is the risk metric, StdDev is returned as an objective measure.

opt_min_var <- optimize.portfolio(
  R = ja_returns, 
  portfolio = min_var,
  optimize_method = "ROI",  
  trace = TRUE
)

Look at the results

print(opt_min_var$data_summary)
## $first
##              SGJ CCC GK
## 2013-01-02 -0.13   0  0
## 
## $last
##             SGJ  CCC   GK
## 2020-01-13 2.23 1.82 1.02
print(opt_min_var$weights)
##       SGJ       CCC        GK 
## 0.3595696 0.2492720 0.3811584

Plot optimized minimum variance

Efficient Frontier

meansd_ef <- create.EfficientFrontier(
  R = ja_returns,
  portfolio = ja_folio ,
  type = "mean-sd",
  n.portfolios = 20,
)

Efficient Frontier

Conclusion - some numbers from a 2016 study

  • An investment of $2000 in an equally weighted portfolio (consisting of CCC, GK and SGJ shares) would result in a return of $9850.96 over a two year period

  • Returns for the CCC from the acquired data revealed a return of 319% and 691% for the years 2013 and 2014 respectively (this is due to a boom in the construction industry)

Reference

Questions

Let’s pRactice